Evaluate
\frac{4x+y}{9x^{2}-4y^{2}}
Expand
-\frac{4x+y}{4y^{2}-9x^{2}}
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\frac{1}{3x-2y}+\frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)}
Factor 9x^{2}-4y^{2}.
\frac{3x+2y}{\left(3x-2y\right)\left(3x+2y\right)}+\frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-2y and \left(3x-2y\right)\left(3x+2y\right) is \left(3x-2y\right)\left(3x+2y\right). Multiply \frac{1}{3x-2y} times \frac{3x+2y}{3x+2y}.
\frac{3x+2y+x-y}{\left(3x-2y\right)\left(3x+2y\right)}
Since \frac{3x+2y}{\left(3x-2y\right)\left(3x+2y\right)} and \frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)} have the same denominator, add them by adding their numerators.
\frac{4x+y}{\left(3x-2y\right)\left(3x+2y\right)}
Combine like terms in 3x+2y+x-y.
\frac{4x+y}{9x^{2}-4y^{2}}
Expand \left(3x-2y\right)\left(3x+2y\right).
\frac{1}{3x-2y}+\frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)}
Factor 9x^{2}-4y^{2}.
\frac{3x+2y}{\left(3x-2y\right)\left(3x+2y\right)}+\frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-2y and \left(3x-2y\right)\left(3x+2y\right) is \left(3x-2y\right)\left(3x+2y\right). Multiply \frac{1}{3x-2y} times \frac{3x+2y}{3x+2y}.
\frac{3x+2y+x-y}{\left(3x-2y\right)\left(3x+2y\right)}
Since \frac{3x+2y}{\left(3x-2y\right)\left(3x+2y\right)} and \frac{x-y}{\left(3x-2y\right)\left(3x+2y\right)} have the same denominator, add them by adding their numerators.
\frac{4x+y}{\left(3x-2y\right)\left(3x+2y\right)}
Combine like terms in 3x+2y+x-y.
\frac{4x+y}{9x^{2}-4y^{2}}
Expand \left(3x-2y\right)\left(3x+2y\right).
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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